A limit result for U-statistics of binary variables

被引：1
|
作者：
Utev, S [1 ]
Becker, NG [1 ]
机构：
[1] La Trobe Univ, Sch Stat Sci, Bundoora, Vic 3083, Australia
来源：
JOURNAL OF THEORETICAL PROBABILITY | 1998年 / 11卷 / 03期
基金：
澳大利亚研究理事会;
关键词：
U-type statistics; binary random variables; law of the iterated logarithm;
D O I：
10.1023/A:1022666901529
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Define r/(k, n) = U-k,U- n - n(k/2)H(k)(Sigma(j =1)(n) X-j/root n), where U-k,U- n = Sigma(1) less than or equal to i(1) not equal ... not equal i(k) less than or equal to n X-i1...X-ik is a symmetric U-type statistic, H-k(.) is the Hermite polynomial of degree k, and {X, X-n, n greater than or equal to 1} are independent identically distributed binary random variables with Pr(X is an element of {-1, 1}) = 1. We show that [GRAPHICS] according as EX = 0 or EX not equal 0, respectively.
引用
收藏
页码：853 / 856
页数：4
相关论文
共 50 条
12345